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A rational expression is similar to a fraction but instead of integers, it contains variables along with numbers. Like a fraction, it comprises a numerator and a denominator. The goal when working with rational expressions is to simplify or reduce them to their simplest form.

Consider the example of \( \frac{100}{25} \). Here, we have an uncomplicated rational expression, which is easy to simplify. The simplest form of a rational expression is achieved when the numerator and the denominator have no common factors other than 1. In this case, both numbers are multiples of 25, which means the expression can be simplified by dividing each term by 25 to arrive at the simplified expression of 4.

It's important to remember that rational expressions can become more complicated when variables are included. For these expressions, simplifying often involves factoring algebraic expressions in the numerator and denominator before dividing.

The top part of a fraction or rational expression is called the numerator, and it indicates the number of parts we're considering. The bottom part, known as the denominator, represents the total number of equal parts into which the whole is divided.

In the rational expression \( \frac{100}{25} \), 100 is the numerator and 25 is the denominator. Understanding the role of each is crucial for simplification. When simplifying, one aim can be to reduce the numerator and the denominator to a point where they no longer share any common factors - this makes the expression easier to work with, especially when resolving equations or performing algebraic division.

Also, when dealing with more complex expressions, always look for the greatest common factor (GCF) to simplify the numerator and denominator. Cancelling out the GCF will lead to the most reduced form of the rational expression.

Algebraic division is the process of dividing algebraic expressions. It is the method we use to simplify rational expressions where the numerator and the denominator often contain variables. The principle is the same as with numerical fractions: divide the numerator by the denominator.

For the straightforward expression \( \frac{100}{25} \), algebraic division simplifies to basic arithmetic, with 100 divided by 25 resulting in 4. However, when variables are involved, we might need to factorize the expressions and cancel out any common algebraic terms in the numerator and the denominator.

Understanding how to perform algebraic division with algebraic expressions is essential for working with polynomial expressions, solving equations, and simplifying complex fractions. It is also an integral part of calculus. The base concept, however, remains simple: divide and simplify.